isrm is 1989 011_parameters controlling rock indentation

8/12/2019 ISRM is 1989 011_Parameters Controlling Rock Indentation

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Rock at Great Depth, Maury & Fourmaintraux (eds), 1989 Ba lkema, Rot te rdam. ISBN 906191975 4

Parameters controlling rock indentation

Parametres de l'action d'une dent d'outil sur les roches

Parameter zur Gesteinseinkerbung

M.ThiercelinSchlumberger Cambridge Research, Cambridge, UK

ABSTRACT:The influence of confining pressure on the indentation response of rocks is analyzed.

Special attention is given to shales which often cause problems during drilling. To take into

account the influence of failure mechanisms during indentation, two indentation parameters aredefined. The first one measures the non-localized deformation under the tooth; in shales, its

value is predicted by a rigid-plastic theory. The second parameter measures the deformation

related to highly localized mechanisms. This parameter is dominant at low confining pressure.

It cannot be predicted by a continuum formulation.

INTRODUCTION

Field observable changes in drilling

response which are related to changes in rock

mechanical properties and environmental


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Table 1

Material properties

Lithology poros. E Uu

% MPa MPa

Carrara marble 0.7 20.700 84.0

Indiana limestone 31.0L. Jur. shale, dry" 8.0 3.200 55.0

L. Jur. shale, sat." 8.0 2.400 17.5

U. Jur. shale" 13.0 1,200 20.0

properties normal to bedding plane.

mechanical behaviour is expected to be very

limi ted. The permeabili t:y of the shales is in

the order of nanoDarcies. Porosity, Young's

modulus at: at:mospheric pressure and uniaxialstr engt h are shown on tabLe 1. Triaxial tests

were carried out to determine the failure

envelope.

EXPERIMENTALPROCEDURE

The equipment used to indent rock samples

under confining pressure comprised a 200

kNLnst.r on mechanical testing machine, a

confining cell, a servo-controlled confining

pressure system and a servo-controlled porepressure system, The cell applied a confining

pressure and pore pressure (up to 60 MPa)to

a 6 inch diameter sample. The simulated mud

pressure which was applied to the top surface

of the sample was equal to the conf ining

pressure (figure 1) .

The samples were protected from

contamination by the confining fluid on

their curved surface by a rubber jacket and

on the surface to be indented by a silicone

visco-elastic putty.

Specific procedures were followed to test

the saturated shale under effective confining

pressure. The high value of the Skempton B

parameter measured in Jurassic shales means

that the application of confining pressure

generates pore pressure close to the confining

pressure. Therefore, the shales had to be

drained in order to achieve high values of

effective stress. To prevent unrealistic

drainage times in these low permeability

rocks, four drainage holes 2.5 inch long

and 0.2 inch in diameter were drilled alongthe axis of the cores, from their bases, to

within one inch of the indentation surface.

The cores were mounted on a permeable disc.

allowing connection of the drainage holes to

the pore pressure control system. Even with

this set-up. the drainage time to achieve a

uniform pore pressure through a sample was at:

least: 14 hours.

The shales were always saturated duringstorage and core preparation. To perform

experiments on dry shales. cores were placed

in an oven at 70 degree Celsius for several

days. Rocks were indented normally to one

surface at a constant displacement rate

of 1 rom/min. Due to sample variability, a

large number of tests had to be performed on

the saturated shales to obtain conclusive

results.

chamber

specimen

Bnud

jacket

Figure 1: The indent:at ion cell.

LOADPENETRATIONCURVESANDFAILURE

MECHANISMS

The load penetration curves obtained during

indentation of these rocks are similar to

those described by Maurer (1965). Cheatham

and Gnirk (1966) and Sikarskie and Cheatham

(1974). At atmospheric pressure. the curves

have a sharply varying slope due to unloading

portions (figure 2). In the literature

this behaviour is called' 'predominantly

bri ttle behaviour' '. Each drop in the load

corresponds to the complete formation of a

chip which is broken free from the specimen.

During loading. the load is often a linearfunct ion of the penet:rat ion.

This "brittle behaviour' , will disappear

progressively with an increase of confining

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pressure. Eventually, at high confining

pressure, a "ductile behaviour" is

observed, which is characterized by a

monotonic load-displacement curve (figure 3) .

1.00.9

0.8

0.7

~ 0.6

:; 0.5< U

.2 0.4

0.3

0.2

0.1

0.0

0.0 1.0 2.0 3.0 4.0

displacement in mm

Figure 2: Load displacement curve of the

LowerJurassic shale at atmospheric pressure.

The failure mechanisms associated with

these macroscopic behaviours are various and

Complex. In the limestones and at atmospheric

pressure, most of the anelastic deformation

which occurs during the loading phase,

takes place in a zone surrounding the tip

of the wedge, where the material is crushed

(Reichmuth, 1963). Tensile microcracking,

crUshing, compaction, and microscopic

Slippage are observed in the anelastic

zone of porous limestones (Thiercelin and

Cook, 1988). Chips correspond to another

modeof deformat ion. They are formed by

the propagation of tensile cracks. Thesemacroscopic tensile cracks are initiated in

the material surrounding the crushed zone and

propagate through intact material.

In the shales, the failure mechanisms are

different (Thiercelin and Cook. 1988). The

deformations are mainly localized along shear

bands and shear cracks, although macroscopic

tensile cracks nucleate close to the rock

surface from the tip of the shear cracks. A

crUshed zone is not observed. However, the

shear cracks are certainly the result of

Strain localization in an anelastic zone.

Under confining pressure, a combination

Of intense anelastic deformation which is

non-localized at a macroscopic level, and

shear cracks, are observed in the marble

and the shales. Surface bulging is produced

around the indentor, rather than discrete

chips. Macroscopically. itbecomes difficult

to differentiate between the deformation

related to the macroscopic shear cracks and

the non-localized anelastic deformation.

Indiana Limestone behaves quite differently

under confining pressure. Cheathamand Gnirk

(1966) observed that the rock deforms mainly

by compaction.

5.0

10.0

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0 5.01.0 2.0 3.0 4.0

displacement in mm

Figure 3: Load displacement curve for the

Lower Jurassic shale at 10 MPa effective

confining pressure.

INDENTATIONPARAMETERS

Indentation parameters are required to

compare the experimental results with

theories. Elasto-plastic theories arecommonlyused to predict the indentation

response. In ductile metals, the slope of

the load-penetration curve characterizes

the indentation response (Hill, 1950). In

rocks, wehave seen that a linear relationship

between load and penetration is either

related to non-localized deformations

at a macroscopic level or to frictional

mechanisms: meanwhile the unloading portion

is always related to highly localized

deformations. Therefore the author proposes

that only the linear loading portion of the

load-penetra,.tion curves can be described

by an elasto-plastic formulation. To study

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the non-localized deformation independently

of the highly localized deformation, two

relevant parameters are proposed. The first

one is related to the linear loading portion

of the load displacement curve and the

second one describes the brittleness of theindentation response.

The first parameter is the mean pressure

Pm acting normal to the original specimen

surf ace. The mean pressure has been def ined

in the literature for ideal plastic materials

which exhibit a linear load penetration curve

when indented by a sharp wedge (Johnston,

1985). For thas e materials, the meanpressure

is:

Pm = F(u)j5(u) (1 )

where:

F (u ) is the load;

5(u) is the tooth cross-section at the

original specimen surface.

5(u) is a furicti.on of the displacement; and the

geometry of the tooth. It is gi ven by:

5(u) = 2wtan(a)u

where:

u is the depth of penetr at ion:

a is the semi-angle of the wedge;

w is the width of the wedge.

Therefore the mean pressure becomes:

J(

Pm =2wtan(a)

where J( is the slope of the load penetration

curve.

However, at low conf ining pressure the

load penetration curve is piecewise linear

in rocks. To keep the notion of measuring

a plastic deformation, we define the mean

pressure as

( 8F(u) 1Pm u) = 8u 2wtan(a)

on the loading portions which are linear. The

meanpressure can be understood as a hardness.

In pratice, one can assume that the mean

pressure is independent of the penetration.

To quantify the complete load displacement

curve an indentation strength (or effective

hardness) is proposed:

1 l o Uam = 2 () F( v) dv

w u tan a 0(5)

where:

u the depth of penetration;

w the width of the wedge;

a the semi -angle of the wedge.

The computation of am is based on the work

done during the indentation. W e often found

that am is independent of the penetrat ion.

However this parameter is still a function

of the mean pressure. To have a better

measurement of the localized deformation

under the tooth, we define the following

parameter:

'" Y= Pm - l.am

(6)

(2)

With this definition ' " Y is equal to zero if

the indentation response is ductile. It is a

measure of the bri ttLenass of the indentation

response.

COMPARISONBETWEENTHEORYANDEXPERIMENTS

(3)

To demonstrat;e that the meanpressure can

be predicted by a plastic formulation,

experimental results are compared with an

analytical solution developed by Cheatham

(1958) for a perfectly plastic material

following a Mohrfailure criterion. Cheatham

obtained the following solutions:

1. for a smooth, perfectly lubricated

tooth-rock interf ace:

1P m =(ap - ac) - 2 . ' "

5111 '

{(1+ sin - (1 - s in the angle of internal friction of

the rock;

ap the peak strength of the rock at a

particular confining pressure;

ac the confining pressure.

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Table 2

Material properties

Lithology q

MPa

90.

52.

57.23.

35.

degree

29.

28.

21.

22.

19.

Carrara marble

Indiana limestone

L. Jur. shale, dry'L. Jur. shale, sat.'

U. Jurassic shale'

properties normal to bedding plane.

2. for a perfectly rough tooth-rock

interface:

1- sin P m = ((7p - (7c) 2costana

{( 1+ ~:::~) (1 + sin )eW - ~~~~} (8)

where w = 2 (a+ f+ ~) tan

To obtain a prediction from the analytical

solution, MohrCoulombfailure parameters

(the uniaxial strength and the internal angle

of friction) are determined for triaxial

testing results. The Mohrfailure criterion

is:

1 1 " (71 =q + tan( - + -) (734 2

q is the intercept of the curve at zero

conr ining pressure. Only the port ion of the

failure curve which is a linear function

of the confining pressure was used to

determine the parameters. Therefore, q

is not necessarily equal to the uniaxial

strength of the material. However, under the

confining pressures tested (up to 100 MPa)

the rocks selected for the study follow such

a criterion. The results of the determinationare shownon table 2.

Acomparison of mean pressures (measured at

atmospheric pressure) with the meanpressure

predicted using the MohrCoulombanalytical

solutions is shownon table 3. The behaviour

of the Lower Jurassic 2 shale was too brittle

at atmospheric pressure to allow us to measure

.its meanpressure. It is observed that, if

one assumes a perfectly rough tooth-rock

interface, the prediction is good for the

Saturated shales and Indiana limestone, and

Underestimated for Carrara marble.

Comparisons between the prediction and the

measurement of the meanpressure as a function

of the confining pressure are shownon figures

4, 5, 6, and 7. The variability of results in

shale is clearly observed and it is typical of

indentation tests. It reflects not only the

sample variability, but also the difficulty of

measuring a single value of the meanpressure

from indentation curves.

500

450

l 1 : l 400c,~ 350c

Q) 300: 5(J) 250(J)

Q)

Ci.200c~ 150

~ 100

50

o

-5 o 5 10 15 20Effective pressure in MPa

25

(9)

Figure 4: Mean pressure as a function of

confining pressure for Lower Jurassic shale,

saturated. Comparison of experiment (0) withprediction (-----).

700

r f . 600~c500Q)

: 5l: l 400Q)

Ci.300cl 1 : l

~ 200

100

800

o

o 5 10 15 20 25 30 35 40 45 5 0

Effective pressure in MPa

Figure 5: Meanpressure as a function of

confining pressure for Lower Jurassic shale,dry. Comparison of experiment (0) with

prediction (------).

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2000

1750

< ll

1500a ..

~

.!: 1250Q): J

1000rJlrJlQ)

a .750

c:< llQ)

500~

250

oo 5 10 15 20 25 30 35 40 45 50

Effective pressure in MPa

Figure 6: Mean pressure as a function

of confining pressure for Carrara marble.

Comparison of experiment (0) with prediction

(--).

2000

1750

< ll

1500a. .

~c:

1250Q)

: J1000rJl

rJlQ)

a .750

c:< llQ)

500~

250

agrees with the measurement only at confining

pressure higher than 10 HPa. However. this

apparent agreement maybe due to sample

variability.

Figures 8 and 9 show the brittleness of

the indentation as a function of confining

pressure for the saturated shale and the

Carrara Marble.

4.0rJlrJlQ)

c:3.0Q)

: E.02.0

6 . 0

5.0

1.0

. ...

o

o 5 10 15 20 25 30 35 40 45 50Effective pressure in MPa

0.0

-5 0 5 10 15 20 25

Effective confining pressure in MPa

Figure 8: Brittleness as a function of

confining pressure for Lower Jurassic shale.

saturated.

rJl

~ 4.0c:Q)

E 3.0: g

Figure 7: Mean pressure as a function of 2.0

confining pressure for Indiana limestone.

Comparison of experiment (0)with prediction 1.0(--).

The predictions are good for the shales.

though at high confining pressures they

are better for the dry shale than for the

saturated shale. This is not the case for the

Indiana Limestone in which the mean pressure

is almost independent of the confining

pressure. For the marble. the prediction

7.0

6. 0

5.0

0.0

-5 5 15 25 35 45

Effective confining pressure in MPa

Figure 9: Bri ttleness as a function of

confining pressure for Carrara marble.

It is found that the experimental values

tend to an' asymptote. In theory. the

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brittleness should tend to zero. These

curves allow us to determine the transition

pressure from a brittle behaviour to a ductile

behaviour. This pressure is obtained once the

brittleness of the indentation response is no

longer a function of the effective confining

pressure. The transition pressure is quitelow for the shale, being around 4 MPa. It is of

the order of 30 MPafor the Carrara Marble.

DISCUSSION

AMohrFailure criterion predicts relatively

well the response of the shales, even

at atmospheric pressure. This is a good

indication that the mean pressure reflects

the macroscopic plastic behaviour of the rock

Under the tooth, at least for shales and at the

~isPlacement rate tested. The meanpressure

as controlled by the uniaxial strength of

the rock, internal friction and the initial

Value of the effective confining pressure.

Use of the mean pressure instead of the

trend of the actual curve (i. e. a parameter

equivalent to the effective hardness defined

in equation (5)) which was used in previous

~ork (Gnirk and Cheatham (1963,1965))

lrnproves the quanti tati ve agreement between

the experimental results and the theory.

Even saturated shales indented at 1 mm/min

fOllow the perfect plasticity prediction.

Oneof the unknowns during the saturated shale

experiments is the behaviour of the saturating

flUid. Fromthis study the agreement between

the theory and the experiments maymean

ei ther that the shale behaviour is drained

at the penetration rate tested. or that

the actual response is similar to a drained

response. The influence of penetration rate

on shale indentation response (Cook and

Thiercelin, 1989) did not allow us to obtainmore definitive conclusions about the pore

fluid behaviour during indentation.

Agood prediction is also achieved for

Carrara marble for pressures higher than

10 MPa. However. a larger number of tests

ls reqUired to reduce the influence of

sample variability on the interpretation.

Indentation of Indiana limestone does not

fOllow such a criterion. Onecan expect that

the compaction of the rock under the tooth is

the Controlling mechanism. To predict the

value of the meanpressure for such a rock.

elasto-plastic models taking into account

compaction during plastic deformation are

Table 3

Comparison between prediction and

experimental results at atmospheric pressure.

The tooth angle is 40 degree except for the

Indiana Limestone (60 degree) .

Lithology smooth rough

MPa MPa

155. 787.

113. 403.

90. 340.

37. 143.

54. 192.

Carrara marble

Indiana limestone

L. Jur. shale. dry

L. Jur. shale, sat.

U. Jur. shale, sat.

exper.

MPa

1690.

351.

brittle

159.

210.

more appropriate than perfect plasticity.

The brittleness of the indentation response

allows us to define accurately the transitionpressure from a brittle behaviour to a ductile

behaviour. This transition is especially

low for the shale tested. This parameter

is more sensitive to the confining pressure

than the meanpressure in the brittle regime.

Therefore one can expect this parameter to be

dominant in rotary drilling at low effective

mudpressure. Unfortunately. even if the mean

pressure can be easily related to intrinsic

rock parameters. this is not the case for

the brittleness. In rotary drilling. the

brittleness of the indentation is not onlya function of rock properties, but also of

mudproperties, penetration rates and tooth

properties.

CONCLUSION

This study has shownthat the indentation

response of rocks can be described by two

parameters: the meanpressure. which is

described by an elasto-plastic theory. and the

bri ttleness of the indentation response whichmeasures the influence of highly localized

deformations. In shales. the mean pressure

is predicted by a perfect plasticity approach,

assuming a Mohrfailure criterion. In porous

limestones one must take into account the

large variation of volume occuring under the

tooth to obtain an accurate prediction.

ACKNOWLEDGEMENT

The author wishes to thank the management of

Schlumberger for permission to publish this

paper.

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REFERENCES

Cheatham J. B. 1958. AnAnalytical Study of

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Proceedings of 8th Drilling and Blasting

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Cheatham J. B. and Gnirk P. F. 1966. The

Mechanics of Rock Failure Associated with

Drilling at Depth. Failure and Breakage of

Rocks, Ed. by C. Fairhurst, AIME,NewYork:

410-439.

Cook J. M. and Thiercelin M. 1989.

Indentation Resistance of Shale; The Effect

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Falconer, I. G. , Burgess, T. M. and Sheppard M.

1988. Separating Bit and Lithology Effects

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17191, proceedings of the IADC/SPEDrilling

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Gnirk P. F. and J .B. Cheatham 1965. An

Experimental Study of Single Bit-Tooth

Penetration Into Dry Rock at Confining

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plasticity, Oxford University Press.

Johnson K.L. Contact Mechanics. Cambridge

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Maurer, W. C. 1965. Bit Tooth Penetration

Under Simulated Borehole Conditions" J.

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Reichmuth, D. R. 1963. Correlation of

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Proc. Fifth Symp. on Rock Mech., Univ. of

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Thiercelin, M. and Cook J. 1988. Failure

Mechanisms Induced by Indentation of Porous

Rock. Proceedings of the 29th U.SRock

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Winters, W. J., WarrenT. M. andOnyaE. C.

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